We remark that the construction of acquisition function has been studied extensively in the case of deterministic ItR [1]}, [2]}, [3]}, [4]}, [5]}, and that there may still be room for improvement relative to (REF ) in the case of uncertain ItR. These potential improvements of acquisition function may generally take consideration of correlation between different \(x\)  in addition to the standard deviation in (REF ). For example, techniques developed for deterministic ItR, such as using a hypothetical point [6]}, [7]} and global sensitivity analysis [2]}, may be transferred here. However, they may lead to significantly increased computational cost when combining with VHGPR (e.g., the re-training of the variational parameters when hypothetical points are used). These potential developments will be left to our future work.
